Article pubs.acs.org/JPCA
Vibrational Relaxation of O2(X3Σ−g , v = 6−8) by Collisions with O2(X3Σ−g , v = 0): Solution of the Problems in the Integrated Profiles Method Shinji Watanabe, Hiroshi Kohguchi, and Katsuyoshi Yamasaki* Department of Chemistry, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan ABSTRACT: The linear kinetic analysis called the integrated profiles method (IPM) makes it simple to analyze the multistep relaxation processes of vibrational manifold. The problem that plots for linear regression in the IPM analysis cannot be made, however, has been found in the study of selfrelaxation of O2(X3Σ−g , v = 6−8). The cause of the problem is the identical time-dependence of the populations of the adjacent vibrational levels. An addition of CF4 into the system made a difference in the time profiles and enabled us to make IPM analysis and determine the rate coefficients. In the experiments, a gaseous mixture of O3/O2/CF4 in an Ar carrier at 298 K was irradiated at 266 nm, and the direct photoproduct O2(X3Σ−g , v = 6−9) from O3 was detected by laser-induced fluorescence (LIF) in the B3Σ−u −X3Σ−g transition. Time-resolved LIF intensities of O2(X3Σ−g , v) at various pressures of O2 and fixed pressure of CF4 were recorded. The resulting rate coefficients for v = 6−8 correlate smoothly with those for v ≤ 5 and v ≥ 8 reported previously. The vibrational-level dependence (v = 2−13) of the rate coefficients for relaxation of O2(X3Σ−g , v) by O2 is accounted for by the balance between the harmonic transition probabilities and the energy defect in the V−V energy-transfer mechanism.
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INTRODUCTION Energy transfer from vibrationally excited molecular oxygen, O2(X3Σ−g , v), to O2(X3Σ−g , v = 0): O2 (v) + O2 (v = 0) → O2 (v − 1) + O2 (v = 1)
vibrational level of interest was recorded. Analysis made by the integrated profiles method (IPM) gave the rate coefficients. We then attempted to extend the vibrational levels to v < 9; however, IPM was not applicable to the low levels because adjacent vibrational levels showed the nearly identical time dependence. We have found that an addition of inert gas with high efficiency of relaxation can be a solution to the problem. A small amount of CF4 made a difference in the time profiles and enabled us to determine the rate coefficients of the levels v = 6−8.
(1)
is important for evaluating the rates of energy disposal in the atmosphere1−3 (upper stratosphere and mesosphere) and controlling plasma.4 Vibrational relaxation of relatively high levels v = 8−27 by O2 has been studied intensively, and the rate coefficients were reported by several groups.1−3,5−12 On the other hand, there have been only two measurements of the rate coefficients of the low vibrational levels v ≤ 5,13,14 and no reports on v = 6 and 7 are present to the best of our knowledge. Kalogerakis et al.13 photolyzed O3 at 266 nm in a mixture of O3/O2 and generated vibrationally excited O2(X3Σ−g , v = 2,3) by rapid conversion from O2(a1Δg) by collisions with O2. They detected O2(X3Σ−g , v = 2,3) by the laser-induced fluorescence (LIF) technique via the B3Σ−u −X3Σ−g transition excited with a tunable ArF laser. A kinetic analysis of the time-resolved LIF intensities of the levels v = 2 and 3 was made, and the rate coefficients for process 1 were determined. Ahn et al.14 employed the stimulated Raman excitation technique to prepare O2(X3Σ−g , v = 1). They excited about 30% of O2 to v = 1 and monitored the time evolution of vibrational distributions of v = 0−5 by spontaneous Raman scattering, determining the rate coefficients for upward and downward vibrational relaxation including the rate coefficients for v = 2−5 of process 1. We have recently reported the rate coefficients for v = 9−13.12 O2(X3Σ−g , v) was generated in the photolysis of O3 at 266 nm, and the time-resolved LIF intensity of a single © 2012 American Chemical Society
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EXPERIMENTAL METHOD The details of the experimental setup have been described in previous papers,12,15,16 and the significant features of the present study are given here. Vibrationally excited O2(X3Σ−g ) was generated in the UV photolysis of O3 at 266 nm with a Nd3+:YAG laser (Spectra Physics GCR-130).17−19 O3 + hν(266nm) → O(3PJ ) + O2 (X3Σ−g )
ϕ ≈ 0.1 (2)
The sample gases (O3/O2/Ar) were flowed in a cylindrical reaction cell made of Pyrex (25 mm in inner diameter). The partial pressures of O2 and O3 in an Ar carrier gas (total pressure: 50 Torr) were 1−6 Torr and 9 mTorr at 298 ± 2 K, and the fluence of the photolysis laser was 1.8 mJ cm−2. Fifty mTorr of CF4 was introduced to make the analysis by IPM Received: May 30, 2012 Revised: July 2, 2012 Published: July 2, 2012 7791
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possible. O2(X3Σ−g , v = 6−9) was detected by LIF in the B3Σ−u − X3Σg− Schumann−Runge system with a Nd3+:YAG laser (Spectra Physics CGR-130)-pumped frequency-doubled dye laser (Lambda Physik LPD3002 with a BBO crystal). The laser dyes, LD489 and C-522B, were used for monitoring v = 6,7 and v = 8,9, respectively. The levels v = 6, 7, 8, and 9 were excited with the rotational lines P(7) (247.94 nm), R(9) (256.89 nm), R(7) (266.34 nm), and R(7) (266.48 nm) of the vibrational bands (0,6), (0,7), (0,8), and (2,9), respectively ((v′,v″) is the notation of vibrational band between the vibrational levels v′ of B3Σ−u and v″ of X3Σ−g ). The fluorescence of the (0, 14) band was monitored for probing v = 6 and 7, (0,17), (0,18), (0,19) bands for v = 8, and (2,18), (2,19), (2,20) bands for v = 9, respectively. The LIF was detected with a high-gain photomultiplier tube (PMT) (Hamamatsu R1104) through bandpass filters, transmittances of which peak at 337 and 400 nm with 10 or 40 nm of full width at half-maximum (fwhm). To record the time profiles of the LIF intensities, the time delays between the photolysis and probe laser were scanned with a pulse delay controller made in house. Fifty Torr of total pressure was sufficient for rapid rotational relaxation within at most 10 ns after the photolysis. LIF intensity excited via a single rotational line, therefore, represents the time evolution of the population in a vibrational level of interest. The typical number of data points in a time profile was 2000, and a step size was varied (50−300 ns) according to the time scales of the profiles. 5−10 time profiles were recorded and averaged to increase the signal-to-noise ratios. O3 was prepared by an electrical discharge in high grade O2 with a synthesizer made in house and was stored in a 3 dm3 glass bulb with Ar (10% dilution). The total pressure of a sample gas was monitored with a capacitance manometer (Baratron 122A). The total pressure measurement together with the mole fractions as measured with calibrated mass flow controllers (Tylan FC-260KZ and STEC SEC-400 mark3) gave the partial pressures of the reagents. High grade O2 (Japan Fine Products, >99.99995%), CF4 (Showa-Denko, 99.99%), and Ar (Japan Fine Products, >99.9999%) were used without further purification.
Figure 1. Time-resolved LIF intensities of the vibrational levels O2(X3Σ−g ): (a) v = 8 and (b) v = 9. (c) IPM plot made from the time profiles shown in (a) and (b). The partial pressures of the sample gases: pO3 = 9 mTorr; pO2 = 5 Torr; and pAr = 45 Torr. The abscissa is the delay time between the photolysis and probe laser. The step size of the time scan was 275 ns. y8(t) and x8(t) are defined by eqs IV and V in the text, respectively.
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molecule−1 s−1 for v = 11;9 therefore, the rate coefficients for v < 11 are expected to be smaller than that for v = 11. In our previous study,12 the upper limit of the rate coefficient for −16 relaxation of v = 8 by Ar, kAr cm3 8 , was estimated to be 5 × 10 −1 molecule−1 s−1, and the rate of diffusion loss, kdiff ≈ 280 s , at 8 50 Torr of Ar was little dependent on v. Under the typical experimental conditions (pO2 ≥ 1 Torr; pO3 = 9 mTorr; and pAr = 50 Torr − pO2) in the present study, the pseudo first-order O rates for the levels v ≤ 8 are estimated to be kv 2[O2] ≥ 5800 −1 O3 −1 −1 Ar s , kv [O3] ≤ 26 s , and kv [Ar] ≤ 800 s . The pseudo first-order conditions [O2(v)] ≪ [M] were satisfied during the present experiments, and the relaxation of O2(v ≤ 22) by O2 proceeds via single-quantum change Δv = 1 (v → v − 1).6,9,10,12 The rate equation for the population of the vibrational level v is given to be:
RESULTS AND DISCUSSION IPM Analysis and Problems. The LIF excitation spectra have been shown in previous papers, (0,6) and (0,7) bands in ref 20, and (0,8) and (2,9) bands in ref 12. Only odd rotational levels appeared according to the statistics of zero nuclear spin of 16O. The time-resolved LIF intensities of v = 8 and 9 are shown in Figure 1a and b, respectively. The kinetic scheme related to the vibrational level v of O2 generated in the photolysis is: k vM+ 1
O2 (v + 1) + M ⎯⎯⎯→ O2 (v) + M k vM
O2 (v) + M ⎯→ ⎯ O2 (v − 1) + M k vdiff
O2 (v) ⎯⎯⎯→ diffusion
(3) (4) (5)
d[v] = −(kvO2[O2 ] + kvQ [Q] + kdiff )[v] dt
kM v
where is the rate coefficient for vibrational relaxation of a level v by collisions with relaxation partner M (=O2, O3, and Ar), and kdiff is the pseudo first-order rate coefficient for v diffusion loss of a level v. The reported rate coefficients for relaxation of O2(X3Σ−g , v = 11−21) by collisions with O3 decrease from 5.5 × 10−12 for v = 21 to 9 × 10−14 cm3
+ (kvO+21[O2 ] + kvQ+ 1[Q])[v + 1]
(I)
kdiff v
where Q = Ar and O3. Here, is replaced with kdiff. According to IPM,21,22 the observed time-resolved LIF intensity of a level v at time t, Iv(t), is given by: 7792
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αv αv + 1
∫0
Article
∫0
t
coefficients is suitable for making a difference in the time profiles I8(t) and I9(t).
Iv(t ′)dt ′
t
Iv + 1(t ′)dt ′
(II)
where αv is a proportionality constant (detectivity) of the level v and Iv(t) = αv[v]. Equation II can be arranged to be:
yv (t ) = −kvxv(t ) + Cv
(III)
where yv (t ) ≡ [Iv(t ) − Iv(0)] xv(t ) ≡
∫0
t
Iv(t ′)dt ′
∫0
∫0
t
Iv + 1(t ′)dt ′
(IV)
t
Iv + 1(t ′)dt ′
kv = kvO2[O2 ] + kvQ [Q] + kdiff Cv = (kvO+21[O2 ] + kvQ+ 1[Q])
αv αv + 1
Figure 2. Vibrational-level dependence of the rate coefficients for 4 from refs 16 and relaxation of O2(X3Σ−g ,v) by CF4 and O2. “●”, kCF v O 20; “○”, kv 2 from ref 12. Note that the scales of the left and right ordinates differ by 3 orders of magnitude.
(V) (VI)
Figure 3a shows the time profiles of v = 8 and 9 in the presence of 50 mTorr of CF4. The partial pressures of O2 and
(VII)
A plot of yv(t) versus xv(t) based on eq III is called an IPM plot, and the slope of the linear regression line gives the pseudo firstorder rate coefficient kv. Figure 1c depicts the plot made from the time profiles of v = 8 and 9 shown in Figure 1a and b. Unfortunately, pseudo firstorder rate coefficient k8 cannot be determined from the plot, because I8(t) and I9(t) are too similar to give time-dependent x8(t). To make a difference between I8(t) and I9(t), measurement of time profiles at different pressures of O2 might be a solution to the problem. However, the timedependences of I8(t) and I9(t) actually are nearly identical over a wide range of [O2], because kOv 2[O2] is the dominant term in kv:kv ≈ kOv 2[O2] ≫ kQv [Q] + kdiff. An alternative solution for making a difference between I8(t) and I9(t) is introduction of an additional relaxation partner to the system. Solution of the Problem by Addition of CF4. The additional relaxation partner is needed to be nonreactive and relax O2(v) via single-quantum change (Δv = 1). The requirement is satisfied by CF4. We have measured the rate coefficients of vibrational relaxation of O2(X3Σ−g , v = 6−12) by CF4:16,20 O2 (X3Σ−g , v) + CF4 (vi = 0) → O2 (X3Σ−g , v − 1) + CF4 (vi = 1) + ΔE
Figure 3. Time-resolved LIF intensities of the vibrational levels O2(X3Σ−g ,v = 8 and 9) in the presence of CF4, (a); and IPM plot made from the time profiles shown in (a), (b). The partial pressures of the sample gases: pO3 = 9 mTorr; pO2 = 5 Torr; pCF4 = 50 mTorr, and pAr = 45 Torr. The step size of the time scan was 135 ns. The red line in (a) shows the result of convolution by eq X. The slope given by a linear regression (red lines in (b)) corresponds to the pseudo first-order decay rates of v = 8, k8, defined by eq VIII. The scales of the ordinate and abscissa are identical to those of Figure 1c.
(6)
reporting that CF4 is more efficient than O2 by about 3 orders of magnitude and the most efficient in the relaxation partners of O2(v = 6−12) studied so far (CO2, NO2, N2O, CH4). The energy defect |ΔE| for the ν3 mode (1281 cm−1) of CF4 is relatively small and decreases from 160 cm−1 (v = 6) to 23 cm−1 (v = 12), and the other three vibrations have large energy defects for v = 6−12: |ΔE| > 395 cm−1 for ν1, >869 cm−1 for ν2, and >672 cm−1 for ν4. In addition to the fundamentals, the energy defects for the overtone and combination levels: |ΔE| > 40 cm−1 for 2ν4, >40 cm−1 for ν1 + ν2, >237 cm−1 for ν1 + ν4, and >237 cm−1 for ν2+ν4, might be candidates for energyaccepting modes of vibration of O2(v = 6−12) because the |ΔE| of 2ν4 and ν1 + ν2 vibrations is as small as those of the ν3 fundamental vibration. Another important feature of relaxation CF by CF4 is that kv 4 for v = 6−12 increases with the vibrational O quantum number v of O2(v)16,20 and kv 2 for v = 8−20 decreases 12 with v, as shown in Figure 2. This countertrend of the rate
Ar are identical to those in Figure 1a and b. In contrast to Figure 1, the time-dependences of v = 8 and 9 differ clearly by addition of CF4 into the system, and, as a consequence, the IPM plot (Figure 3b) shows a linear correlation between y8(t) and x8(t). It should be noted that the ranges of the ordinates and abscissas in Figures 1c and 3b are identical. When CF4 is introduced to the system, eqs VI and VII are replaced with the following equations: 7793
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kv = kvO2[O2 ] + kvCF4[CF4] + kvQ [Q] + kdiff Q 4 Cv = (kvO+21[O2 ] + kvCF + 1[CF4 ] + k v + 1[Q])
single-quantum change (Δv = 1). The time profiles of other vibrational levels v = 6 and 7 were analyzed in the same manner, and the rate coefficients kO6 2 and kO7 2 have been determined to be [3.2 ± 0.4(2σ)] × 10−13 and [2.9 ± 0.3(2σ)] × 10−13 cm3 molecule−1 s−1, respectively. Rate Coefficients for Vibrational Relaxation of O O2(X3Σ−g , v = 2−13) by O2. The rate coefficients kv 2 for v = 6−8 determined in the present study are listed in Table 1 together with those for v = 2−5 and 8−11 reported previously. kOv 2 for v = 6 and 7 are measured for the first time in the present study. Klatt et al.10 generated vibrationally excited O2 by a chemical reaction, O(3P) + NO2 → O2(v ≤ 11) + NO, and analyzed the time profiles of O2(v) by the multiexponential analysis to give the rate coefficients for the level v = 8−11. Their value for v = 8 is in good agreement with ours despite the different methods for generation of O2(v) and the kinetic analysis. Figure 5a shows vibrational-level dependence of kOv 2 over the levels v = 2−13. Kalogerakis et al.13 reported kOv 2 for v = 2 and 3 at 330 K. They prepared O2(X3Σ−g , v = 2,3) by rapid conversion from O2(a1Δg,v ≤ 3) generated in the UV photolysis of O3. The effect of cascading from higher levels (v > 3), which were generated in the minor photolysis channel O3 + hν → O2(X3Σ−g ) + O(3P), was taken into account to give kO2 2 and kO3 2. Ahn et al.14 performed experiments and calculations and reported three sets of results on the rate coefficient kOv 2 for v = 2−5. Their experimental values show strong dependence on the vibrational levels, and that for v = 4 is extraordinarily large (Figure 5a). They also found that semiclassical trajectory calculations are likely to underestimate the rate coefficients by about a factor of approximately 10, suggesting that results on the forced harmonic oscillator model with pure repulsive potential23 should be multiplied by 8 and that the contribution of the attractive part of short-range potential24 should be enlarged by 175%. The values of the rate coefficients kOv 2 appear to peak at around v = 5. The turnover of the rate coefficients is accounted for by the balance between the vibrational-level dependence of the transition probability and the energy defect in relaxation. The simple model of vibrational energy transfer between harmonic diatomic molecules and atoms, based on Landau− Teller (LT) model and Schwartz−Slawsky−Herzfeld (SSH)
(VIII)
αv αv + 1
(IX)
The slope of the linear regression line (red line in Figure 3b) gives the pseudo first-order rate coefficient k8. We also have recorded the time profiles of v = 8 and 9 at different O2 pressures and analyzed them in the same way by IPM. A resulting plot of k8 versus [O2] is shown in Figure 4. The
Figure 4. [O2]-dependence of the pseudo first-order decay rate of v = 8. The slope given by a linear regression gives the bimolecular rate coefficient for vibrational relaxation of O2(X3Σ−g ,v = 8) by O2(X3Σ−g ,v = 0).
bimolecular rate coefficient for vibrational relaxation of v = 8 by O2, kO8 2, has been obtained from the slope of the plot to be [2.0 ± 0.2(2σ)] × 10−13 cm3 molecule−1 s−1. The relatively large 4 intercept at 3000 s−1 of the plot corresponds to kCF 8 [CF4] + O3 20 CF4 kAr [Ar] + k [O ] + k . From the rate coefficients, k 8 8 3 diff 8 = 1.4 −16 3 −1 −1 × 10−12, kO8 3 < 9 × 10−14, kAr ≤ 5 × 10 cm molecule s , 8 −1 and kdiff ≈ 280 s , the value of intercept is estimated to be 6, as seen in Figure 5b. The findings strongly suggest that the energy transfer between O2(v) and O2 is governed dominantly by V−V mechanism. The deflection of v < 6 from the line extrapolated from the adiabatic regime indicates that v < 6 is in the diabatic regime.
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Figure 5. Vibrational-level dependence of the rate coefficients of O O O2(X3Σ−g ,v) by O2: (a) kv 2 versus v and (b) In(kv 2·v−1) versus |ΔE| for V−V mechanism. The “◑” correspond to ref 13, the “□” to experimental values in ref 14, the “◇” to semiclassical predictions with forced oscillator model (ref 23) multiplied by 8, the “△” to semiclassical calculation (ref 24) with the short-range attractive part increased by 175%, the “○” to ref 10, the “▲” to ref 12, and “●” to this work. The broken line in (b) is the result of linear regression using the data for v = 6−13 reported by the author’s group.
SUMMARY A critical problem of the IPM analysis has been found in the kinetic study on the vibrational relaxation of O2(X3Σ−g , v = 6− 8) by collisions with O2. The cause of the problem is the identical time-dependence of the populations of the adjacent vibrational levels v and v + 1, and the resulting IPM plots do not show a linear correlation. The introduction of CF4, which is chemically inert and efficient at relaxation of O2, makes a difference in the time profiles and enables the IPM analysis. The effect of O2 on relaxation was extracted from the measurements of [O2]-dependence at fixed concentration of CF4. The present results smoothly connect the rate coefficients for the low v ≤ 5 and high v ≥ 9 vibrational levels reported so far. The bimolecular rate coefficients for relaxation of O2(v = O 2−13) by O2, kv 2, peak at around v = 5. The vibrational-level dependence is accounted for by the balance of the harmonic transition probability, kOv 2 ∝ v, and the energy defect due to anharmonicity, kOv 2·v−1 ∝ exp(|ΔE|), where |ΔE| is the energy defect of the process. For the V−V mechanism, kOv 2 increases with v at the low vibrational levels with small |ΔE|, although kOv 2 decreases with v at high vibrational levels because exp(−|ΔE|) decreases with v. The present success in solving the problem in the IPM analysis extends the ability of the linear analysis for the studies on chemical kinetics.
theory, shows that the rate of relaxation (transition probability) is in proportion to vibrational quantum number kOv 2 ∝ v, that is, kOv 2·v−1 ≈ constant.25,26 Figure 5b, however, shows that kOv 2·v−1 is not constant but decreases with v, suggesting that the energy defect due to anharmonicity is the cause of the vibrational-level dependence of kOv 2·v−1. The correlation between kOv 2·v−1 and v is based on the adiabaticity of the energy-transfer process. The efficiency of energy-transfer process is evaluated by the adiabaticity parameter.27 ζ=
a|ΔE| hv
(XI)
where a is an action length between two molecules; h is Planck’s constant; v is a relative velocity; and |ΔE| is an energy defect of the process. |ΔE| also represents energy converted between vibration and translation. The adiabaticity parameter gives criteria for energy-transfer process: ζ > 1 corresponds to the adiabatic regime and ζ < 1 to the diabatic regime, respectively.27 If the relaxation of O2(v) by O2 proceeds via a vibration-to-translation (V−T) mechanism, |ΔE| corresponds to the energy spacing between adjacent vibrational levels ΔGv+1/2 defined by G(v + 1) − G(v), where G(v) is the term value of a vibrational level v. ΔGv+1/2 decreases from 1533 cm−1 for v = 2 to 1282 cm−1 for v = 13, and the corresponding ζ also decreases from 14.6 for v = 2 to 12.2 for v = 13 using a ≈ 0.2 nm27 and v = 630 ms−1 at 298 K. ζ ≫ 1 indicates that the energy transfer between O2(v = 2−13) and O2 is in the adiabatic regime as long as the relaxation is governed by the V−
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AUTHOR INFORMATION
Corresponding Author
*Fax: +81-82-424-7405. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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